{"docId":5106,"paperId":5106,"url":"https:\/\/hrj.episciences.org\/5106","doi":"10.46298\/hrj.2019.5106","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986071","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01986071v1","dateSubmitted":"2019-01-23 14:14:43","dateAccepted":"2019-01-23 15:31:08","datePublished":"2019-01-23 15:31:19","titles":{"en":"On-Regular Bipartitions Modulo $m$"},"authors":["Somashekara\n, \nD D","Vidya\n, \nK N"],"abstracts":{"en":"Let $b_l (n)$ denote the number of $l$-regular partitions of $n$ and $B_l (n)$ denote the number of $l$-regular bipartitions of $n$. In this paper, we establish several infinite families of congruences satisfied by $B_l (n)$ for $l \\in {2, 4, 7}$. We also establish a relation between $b_9 (2n)$ and $B_3 (n)$."},"keywords":[{"en":"05A17"},{"en":"Congruence"},{"en":"partition"},{"en":"regular partition"},{"en":"regular bipartition"},{"en":"theta functions 2010 Mathematics Subject Classification 11P83"},"\n[\nMATH\n] \nMathematics [math]","\n[\nMATH.MATH-NT\n] \nMathematics [math]\/Number Theory [math.NT]"]}